I find a interesting question of Prmo mock and Promys 2020

For which $n\in\mathbb{N}$ is it possible to arrange $\{1,…,n^2\}$ in an $n\times n$ grid so that the set of products of columns equals the set of products of rows?

I can find solution for $3\times 3$ or $4\times 4$ but unable to generalize for $n\times n$.

The question has been answered by Rob Pratt but I am unable to understand his solution .

Can anyone please help me in this question